Electromagnetic Induction
Part of Electrical Theory
How changing magnetic fields create electrical voltage—the principle behind generators, transformers, and inductors.
Why This Matters
Electromagnetic induction is the physical principle that makes large-scale electrical civilization possible. Every generator, from a hand-cranked bicycle dynamo to a multi-megawatt hydroelectric turbine, works by electromagnetic induction. Every transformer—the device that makes long-distance power transmission economically viable—works by electromagnetic induction. Every inductor in every filter circuit operates through this principle.
Michael Faraday discovered electromagnetic induction in 1831 after years of trying to make magnetism produce electricity (the reverse of what he already knew: that electricity could produce magnetism via Ørsted’s discovery). His success made possible everything that followed. A rebuilding community that understands this principle can build generators from wire, magnets, and basic mechanical skill—no exotic materials required.
Faraday’s Discovery
Faraday found that:
- Moving a permanent magnet into a coil of wire caused a brief deflection of a galvanometer connected to the coil
- Moving the magnet out caused the galvanometer to deflect in the opposite direction
- Holding the magnet stationary inside the coil produced no deflection at all
- Moving the coil instead of the magnet produced the same result—only relative motion mattered
The key insight: it is the change in magnetic flux through the coil, not the presence of a magnetic field, that induces voltage. A static magnetic field, no matter how strong, produces no EMF in a stationary conductor.
Faraday’s Law
EMF = -N × dΦ/dt
Where:
- EMF = induced electromotive force (voltage) in volts
- N = number of turns in the coil
- Φ = magnetic flux through one turn (in webers)
- dΦ/dt = rate of change of flux (webers per second)
- The negative sign indicates the induced EMF opposes the change (Lenz’s Law)
Magnetic flux Φ = B × A × cos θ
Where:
- B = magnetic field strength (tesla)
- A = area of the coil (m²)
- θ = angle between the magnetic field and the coil’s normal (perpendicular to the coil face)
How a Generator Works
A generator rotates a coil in a magnetic field. As the coil rotates, the angle θ between the field and the coil normal changes continuously. The flux Φ = B × A × cos θ varies sinusoidally. The rate of change dΦ/dt is also sinusoidal, leading to a sinusoidal output voltage.
Output voltage of a simple AC generator: V(t) = N × B × A × ω × sin(ωt)
Where ω = 2πf is the angular velocity (radians per second).
Peak voltage: V_peak = N × B × A × ω
To increase generator output:
- More turns N → proportional increase
- Stronger field B → proportional increase
- Larger coil area A → proportional increase
- Higher rotation speed ω → proportional increase
Practical generator design: The simplest generator is a wire loop rotating between permanent magnet poles. With 100 turns, a field of 0.5 tesla, a coil area of 100 cm² (0.01 m²), rotating at 50 Hz (ω = 314 rad/s):
V_peak = 100 × 0.5 × 0.01 × 314 = 157V
This is achievable with a modest permanent magnet salvaged from industrial equipment or a carefully designed electromagnet.
How a Transformer Works
A transformer uses electromagnetic induction between two coils sharing a common iron core.
When AC current flows in the primary coil, it creates a changing magnetic flux in the iron core. This changing flux passes through the secondary coil. By Faraday’s Law, a voltage is induced in the secondary proportional to the number of secondary turns.
Transformer equations: V₂/V₁ = N₂/N₁ (voltage ratio equals turns ratio) I₁ × N₁ = I₂ × N₂ (current ratio is inverse of turns ratio, for ideal transformer) V₁ × I₁ = V₂ × I₂ (input power equals output power for ideal transformer)
Why AC only: The flux in the core must be changing for voltage to be induced in the secondary. DC creates constant flux—no induction. A transformer connected to DC will simply have a resistive primary coil drawing current, with no output from the secondary.
Core material: Iron greatly concentrates magnetic flux (high permeability), allowing a given number of coil turns to create far more flux than an air core would. This reduces the number of turns needed to a practical level. The iron core is made from thin laminated sheets rather than a solid block to reduce eddy current losses (currents induced in the core itself by the changing flux, which would waste energy as heat).
Self-Induction and Inductors
When the current in a coil changes, the changing current creates a changing magnetic flux, which induces a voltage in the same coil. This is self-induction.
The voltage across an inductor: V = L × dI/dt
Where L is the inductance in henries.
This induced voltage opposes the change in current (Lenz’s Law): rising current induces a back-voltage opposing the rise; falling current induces a forward voltage trying to maintain the current.
Practical consequences:
- An inductor in series with a load smooths current changes—it is an AC current filter
- Switching off a DC circuit containing an inductor (motor, relay) causes a voltage spike potentially many times the supply voltage, as the inductor tries to maintain its current
- Motor starting current is high because the inductor’s back-EMF has not yet built up to oppose current flow
- Transformer inrush current on first energization is high for the same reason
Mutual Induction
When two coils are near each other, a changing current in one (the primary) induces voltage in the other (the secondary). This is mutual induction—the basis of the transformer, but also of inductive coupling between any adjacent conductors.
Mutual inductance M quantifies the coupling: V₂ = M × dI₁/dt
Coupling coefficient k: M = k × √(L₁ × L₂), where 0 ≤ k ≤ 1. For a tightly coupled transformer with a closed iron core: k ≈ 0.99 or better. For loosely coupled air-core coils: k may be 0.01 or less.
Parasitic coupling: Two adjacent wires carrying different signals are mutually coupled. This is how interference enters a circuit from a neighbor—the changing current in one wire induces a small voltage in the adjacent wire. Shielding (a grounded conductor surrounding the signal wire) interrupts this inductive coupling. Twisting wires together ensures any mutual coupling is equal and opposite in the two conductors, canceling at the differential input.
Lenz’s Law in Detail
Lenz’s Law states: the induced current opposes the change that caused it.
This is the physical content of the negative sign in Faraday’s Law. Consequences:
Magnetic braking: Moving a conductive plate through a magnetic field induces currents (eddy currents) in the plate. These currents create their own magnetic field opposing the motion—a braking force. This is the principle of eddy current brakes on laboratory balances, electromagnetic door holders, and railway braking systems.
Damped galvanometer: When a galvanometer needle moves, the coil rotates in the magnetic field, inducing a current. This current creates a force opposing the motion, damping the oscillation. Properly damped, the needle settles at the correct reading without excessive oscillation—critical for fast, accurate readings.
Power generation requires force: Because a generator’s output current creates a field opposing the rotor motion, power generation requires mechanical force to maintain rotation. More electrical load = more opposing force = more mechanical power needed. This is the physical connection between mechanical input power and electrical output power in any generator.